Advertisements
Advertisements
प्रश्न
Find the angles marked with a question mark shown in Fig. 17.27
Advertisements
उत्तर
\[\text{ In } \bigtriangleup CEB: \]
\[\angle ECB + \angle CBE + \angle BEC = 180° (\text{ angle sum property of a triangle })\]
\[40° + 90° + \angle EBC = 180° \]
\[ \therefore \angle EBC = 50° \]
\[\text{ Also }, \angle EBC = \angle ADC = 50° \left( \text{ opposite angle of a parallelogram } \right)\]
\[\text{ In } \bigtriangleup FDC: \]
\[\angle FDC + \angle DCF + \angle CFD = 180° \]
\[50° + 90° + \angle DCF = 180° \]
\[ \therefore \angle DCF = 40° \]
\[\text{ Now }, \angle BCE + \angle ECF + \angle FCD + \angle FDC = 180° (\text{ in a parallelogram, the sum of alternate angles is } 180° )\]
\[50° + 40° + \angle ECF + 40° = 180° \]
\[\angle ECF = 180° - 50° + 40° - 40° = 50° \]
संबंधित प्रश्न
All rhombuses are parallelograms.
Name the quadrilaterals whose diagonals are perpendicular bisectors of each other
The sum of two opposite angles of a parallelogram is 130°. Find all the angles of the parallelogram.
Which of the following statement is true for a rhombus?
Its diagonals are equal and perpendicular.
Construct a rhombus whose diagonals are of length 10 cm and 6 cm.
If opposite angles of a rhombus are (2x)° and (3x - 40)° then value of x is ______.
Lengths of diagonals of a rhombus ABCD are 16 cm and 12 cm. Find the side and perimeter of the rhombus.
The given figure shows a rhombus ABCD in which angle BCD = 80°. Find angles x and y.
A Rangoli has been drawn on a flor of a house. ABCD and PQRS both are in the shape of a rhombus. Find the radius of semicircle drawn on each side of rhombus ABCD.
Construct a rhombus CLUE in which CL = 7.5 cm and LE = 6 cm.
